Probability and Learning

A$.$ Let us consider this simplified model of the climate.

The climate pattern can either be El Ni$$o $(1/3$ of the time$)$ or La Ni$$a

$(\frac{2}{3}$ of the time$).$

In Illinois, El Ni$$os tend to have more rain and La Ni$$as tend to have

less rain.

In Brazil, El Ni$$os tend to have less rain and La Ni$$as tend to have

more rain.

For both Illinoisan and Brazilian farmers, if they have more rain then

they tend to grow more soy. If they have less rain then they tend to

grow less soy.

If Illinoisan farmers grow more soy, then global price of soy tends to go

down. If Illinoisan farmers grow less soy, then global price of soy tends

to go up$.$

If Brazilian farmers grow more soy, then global price of soy tends to go

down. If Brazilian farmers grow less soy, then global price of soy tends

to go up$.$

If Illinoisan farmers grow more soy then they tend to be happier.

If the global price of soy goes up then Illinoisan farmers tend to be

happier.

If Brazilian farmers grow more soy then they tend to be happier.

If the global price of soy goes up then Brazilian farmers tend to be

happier.

Construct a Bayesian Network that describes the relation among the

variables

Give this Bayesian Network conditional or prior probability values at

each node from the data above and reasonable assumptions. Please

state your assumptions.

If you are told about the how much rain Illinoisan farmers received,

and the global price of soy, do you need to know anything about the

Brazilian rainfall or soy output to know about the happiness of

Illinosian farmers? Explain.